ON REGULARIZATIONOFLEASTSQUAREPROBLEMS VIAQUADRATICCONSTRAINTS
Majid Fozunbal · 2007
We consider uncertainty reduction inleast square problems raised insystem identification withunknown state space. We assume existence ofsomeprior information obtained through afinite series ofmeasurements. Thisdataismodeled inthe formofafinite collection ofquadratic constraints enclosing thestate space. A simple closed formexpression isderived fortheoptimal solution featuring geometric insights andintuitions that reveal atwo-fold effort inreducing uncertainty: by correcting theobservation error andbyimproving thecondition number ofthedata matrix. Todeal withthedual problem offinding theoptimal Lagrange multipliers, weintroduce an approximate, positive semidefinite program that canbeeasily solved using thestandard numerical techniques. IndexTerms-Identification, least squares methods, linearsystems, uncertainty, andregularization.